113 LearnersLast updated on May 26th, 2025
Cube Root of 106480
A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 106480 and explain the methods used.
What is the Cube Root of 106480?
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.
In exponential form, ∛106480 is written as (1064801/3). The cube root is just the opposite operation of finding the cube of a number. For example, assume ‘y’ as the cube root of 106480, then \(y^3\) can be 106480. The cube root of 106480 is not an exact integer, but it can be written as approximately 47.512.
Finding the Cube Root of 106480
Finding the cube root of a number is to identify the number that must be multiplied by itself three times to result in the target number. Now, we will go through the different ways to find the cube root of 106480. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
To find the cube root of a non-perfect number, we often follow Halley’s method. Since 106480 is not a perfect cube, we use Halley’s method.
Cube Root of 106480 by Halley’s method
Let's find the cube root of 106480 using Halley’s method.
The formula is ∛a ≅ x(frac{(x3 + 2a)}{(2x3 + a)})
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting, a = 106480;
x = 47
∛a ≅ 47(frac{(473 + 2 × 106480)}{(2 × 473 + 106480)})
∛106480 ≅ 47.512
The cube root of 106480 is approximately 47.512.
Common Mistakes and How to Avoid Them in the Cube Root of 106480
Finding the cube root of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes that students commonly make and ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Children often try to calculate an exact whole number for the cube root of numbers like 106480, which are not perfect cubes.
For example, they assume that they would get an exact whole number for 106480 like they get for 64 (since ∛64 = 4). To avoid this error, remember that some numbers don't have a perfect cube root, and the cube root of 106480 is approximately 47.512.
Cube Root of 106480 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 106480 cubic centimeters. Find the length of one side of the container equal to its cube root.
Side of the cube = ∛106480 ≈ 47.512 units
Explanation
To find the side of the cube, we need to find the cube root of the given volume.
Therefore, the side length of the cube is approximately 47.512 units.
Problem 2
A construction project requires 106480 cubic meters of material. Calculate the amount of material left after using 1000 cubic meters.
The amount of material left is 105480 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
106480 - 1000 = 105480 cubic meters.
Problem 3
A tank holds 106480 cubic meters of water. Another tank holds a volume of 2000 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 108480 cubic meters.
Explanation
Let’s add the volume of both tanks:
106480 + 2000 = 108480 cubic meters.
Problem 4
When the cube root of 106480 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 47.512 ≈ 95.024 The cube of 95.024 ≈ 857218.5
Explanation
When we multiply the cube root of 106480 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(53000 + 53480).
∛(53000 + 53480) = ∛106480 ≈ 47.512
Explanation
As shown in the question ∛(53000 + 53480), we can simplify that by adding them.
So, 53000 + 53480 = 106480.
Then we use this step:
∛106480 ≈ 47.512 to get the answer.
FAQs on Cube Root of 106480
1.Can we find the Cube Root of 106480?
2.Why is the Cube Root of 106480 irrational?
3.Is it possible to get the cube root of 106480 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube Root of 106480?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube Root of 106480?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Cube Root of 106480
- Cube root: The number that is multiplied by itself three times to get the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example, 3 × 3 × 3 = 27, therefore, 27 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (1064801/3), ⅓ is the exponent, which denotes the cube root of 106480.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of 106480 is irrational because its decimal form goes on continuously without repeating the numbers.
Explore More algebra
Previous to Cube Root of 106480
About BrightChamps in Saudi Arabia
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
